KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Journal of the Australian Mathematical Society

VOLODYMYR MAZORCHUK¹ 

关键词: primary 16S37;    secondary 16E30;    16G10;   

DOI  :  10.1017/S1446788710001497

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.

【 授权许可】

Unknown